A new crop of ultra-luxurious New York high rises are vying to be the next hot “it” building and are attracting billionaires from nearby as well as abroad.

Walking slowly to the windows facing the meadow of green that is Central Park, Gary Barnett slips into salesman mode as he spreads his arms wide, embracing the sweeping bird’s-eye view he has from the 87th floor of his shimmering skyscraper in Midtown Manhattan.

Noting a visitor’s gasp at the stunning vista, he smiles. “That’s what we want. We want the ‘Oh, wow,’ ” he says.

That ‘oh wow’ factor is part of a 6,250-square-foot, full-floor apartment in his soaring skyscraper, One57, complete with a soon-to-arrive master bedroom tub carved from a single piece of Italian marble. The apartment comes with a hefty price tag of $67 million. Or, put another way, nearly $11,000 per square foot. That’s Per. Square. Foot.

Too rich? Well, there is another, similar apartment a few floors lower that has a number of potential buyers circling it that’s “only $55 million,” Mr. Barnett says before pausing. “I didn’t really say, only $55 million?” He laughs. “It’s all relative.”